Table Of Content~ 7 secnavdA ni remyloP ecneicS
Conformational Motion
and Disorder in
Low and High Molecular
Mass Crystals
M. B.Wunderlich, By ,re116M
.J GrebowiHc.z , Baur
With 24 Figures and 11 Tables
galreV-regnirpS Berlin Heidelberg kroYweN
London Paris Tokyo
Bernhard Wunderlich
Department of Chemi~l~ .~ F he University of Tennessee, Knoxville,
TN 37996-1600, USA
Martin re116M
Institut filr Makromolekulare Chemie, Universit/it Freiburg,
D-7800 Freiburg, FRG
Janusz Grebowicz
Dept. Polymer Science and Engineering, University of Massachusetts,
Amherst, MA 01003, USA
Herbert Baur
Kunststofflaboratorium, BASF AG, D-6700 Ludwigshafen, FRG
ISBN-3-540-18976-9 Springer-Verlag Berlin Heidelberg New York
ISBN-0-387-18976-9 Springer-Verlag New York Heidelberg Berlin
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Editors
Prof. Henri CNRS, Benoit, Centre de sur Recherches sel Macromolecules, ,6
rue Boussingault, 38076 Strasbourg France Cedex,
Prof. Hans-Joachim Cantow, Institut ftir Makromolekulare der Chemic Uni-
Stefan-Meier-Str. versit/it, ,13 Freiburg 7800 .i Br., FRG
Prof. Gino Dall'Asta, aiV Pusiano ,03 73102 Milano, Italy
Prof. Karel Dugek, Institute of Macromolecular Chemistry, Czechoslovak
Academy of ,secneicS 60261 Prague CSSR 616,
Prof. Hiroshi Fujita, 53 Shimotakedono-cho, Shichiku, Kita-ku, Kyoto ,306
Japan
Prof. Gisela Chemical Department, Henrici-Oliv6, University of California,
San Diego, La Jolla, CA ,73029 U.S.A.
Friedrich-Schiller-Universi- Chemie, Prof. Dr. Sektion G/inter Heublein, habil
t/it, HumboldtstraBe ,01 96 Jena, DDR
Prof. Dr. Hartwig H6cker, Deutsches Wollforschungs-Institut .e .V an der
Aachen, Hochschule Technischen Veltmanplatz ,8 Aachen, 5100 FRG
Prof. Hans-Henning Kausch, Polytechnique Laboratoire Ecole de Polym6res,
de Lausanne, F6d6rale ,23 .hc de Bellerive, 7001 Lausanne, Switzerland
Prof. Joseph .P Kennedy, Institute of Polymer The Science, University of
Akron, Akron, Ohio ,52344 U.S.A.
Prof. Anthony D Laboratories, Lathom & R plc, Brothers Pilkington Ledwith,
Ormskirk, Lancashire 04L 5UF UK
Prof. Seizo Okamura, No. ,42 Minamigoshi-Machi Okazaki, Sakyo-Ku.
Kyoto ,606 Japan
Prof. Salvador Oliv6, Chemical Department, University of California,
San Diego, La ,aUoJ CA ,73029 U.S.A.
Prof. Charles G. Overberger, Department of Chemistry. The University of
Michigan, Ann Arbor, U.S.A. 48109, Michigan
Ringsdorf, Helmut Prof. Institut Johannes-Gutenberg- Chemie, Organische fiJr
J.-J.-Becher Universit/it, geW Mainz, 6500 18-20, FRG
Prof. Takeo Saegnsa, Department of Synthetic Chemistry, Faculty of
Kyoto Engineering, Yoshida, University, Kyoto, Japan
Prof. John .L Schrag, University of Wisconsin, Department of Chemistry,
1011 Avenue, Madison, University Wisconsin ,60735 U.S.A.
Prof. G/inter Niklas-Vogt Victor Schulz, e3lartS ,22 Mainz, 6500 FRG
Prof. William .P Slichter, Executive, Director, Research-Materials Science
and Division Engineering AT Laboratories, T Bell & 006 Mountain Avenue,
Murray Hill, NJ ,47970 U.S.A.
Prof, John Department K. Stille, of University, Colorado State Chemistry. Fort
Colorado Collins, ,32508 U.S.A.
Table of Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . 1
1.1 Definition of Condis Crystals and an Approximate
Empirical Transition Entropy Description ..... 1
1.2 Justification of the Empirical Transition Entropy
Description . . . . . . . . . . . . . . . . . . . 3
1.3 Motion in the Condensed Phase . . . . . . . . . . 3
1.4 Summary and Conclusions . . . . . . . . . . . . 6
2 Thermodynamics of the Conformationai Isomerism .... 7
2.1 Dynamic Effects of the Conformational Isomerism. 8
2.2 Thermostatic Effects of the Conformational Isomerism 10
2.3 Summary and Conclusions . . . . . . . . . . . . 25
3 Condis Crystals of Cyclic Alkancs, Silanes and Related
Compounds . . . . . . . . . . . . . . . . . . . . . 26
3.1 Cycloalkanes . . . . . . . . . . . . . . . . . . 26
3.1.1 Plastic Crystals (C2H4 to C9Hls) . . . . . . . 26
3.1.2 Condis Crystals (CloH2o to C32H64 ) . . . . . . 32
3.1.3 Rigid Crystals (C36H72 to Polyethylene) .... 37
3.2 Substituted Cycloalkanes . . . . . . . . . . . . . 39
3.3 Other Ring Compounds . . . . . . . . . . . . . 40
3.4 Summary and Conclusions . . . . . . . . . . . . 43
4 Condis Crystals of Flexible Macromolecules . . . . . . . 44
4.1 Polyethylene and n-Paraffins . . . . . . . . . . . 45
4.2 Polytetrafluoroethylene and n-Perfluoroalkanes . . . 50
4.3 Other Fluoropolymers of Type CF2-CXY . . . . . . 54
4.4 Polypropylene . . . . . . . . . . . . . . . . . 57
4.5 Polydienes . . . . . . . . . . . . . . . . . . . . 59
4.6 Other Flexible Carbon-Backbone Macromolecules . . 62
4.7 Polydialkylsiloxanes . . . . . . . . . . . . . . . 64
4.8 Polyphosphazenes . . . . . . . . . . . . . . . . 65
4.9 Summary and Conclusions . . . . . . . . . . ... 66
5 Condis Crystals and Their Relation to Liquid Crystals... 67
5.1 Poly-p-phenylenes . . . . . . . . . . . . . . . . 67
5.1.1 Benzene and Related Compounds . . . . . . 67
VIII Table of Contents
5.1.2 Biphenyl and Terphenyl . . . . . . . . . . . 70
5.1.3 Quaterphenyl and Higher Oligomers ..... 72
5.1.4 Polyparaphenylene . . . . . . . . . . . . . 73
5.2 Low Molecular Mass Liquid Crystals . . . . . . . 73
5.2.1 Molecules with Rod-Like Mesogens ...... 73
5.2.2 Molecules with Disk-Like Mesogens ..... 77
5.2.3 Amphiphilic Molecules . . . . . . . . . . . 79
5.3 Macromolecules with Rigid and Flexible Segments 85
5.3.1 Polymers without Liquid Crystalline Phases . . 86
5.3.2 Liquid Crystalline Polymers with Main-Chain
Mesogens . . . . . . . . . . . . . . . . . 88
5.3.3 Liquid Crystalline Polymers with Side-Chain
Mesogens . . . . . . . . . . . . . . . . . 90
5.3.4 Macroscopic Mesogens with Flexible Side-Chains 92
5.4 Summary and Conclusions . . . . . . . . . . . . 94
Condis Crystals of Stiff Macromolecules . . . . . . . . 96
6.1 Chain Extension and Flexibility . . . . . . . . . . 96
6.2 Strictly Linear Macromolecules . . . . . . . . . . 98
6.3 Polyoxybenzoate and its Copolymers . . . . . . . . 99
6.4 Aromatic Polyamides . . . . . . . . . . . . . . 101
6.5 Summary and Conclusions . . . . . . . . . . . . 102
7 Conclusions . . . . . . . . . . . . . . . . . . . . 103
8 Acknowledgements . . . . . . . . . . . . . . . . . 104
9 References . . . . . . . . . . . . . . . . . . . . . 104
Author Index Voimes 1-87 . . . . . . . . . . . . . . 123
Subjectlndex . . . . . . . . . . . . . . . . . . . . 135
The broad field of conformational motion and disorder in crystals is reviewed with attention
paid to the distinction of the recently defined condis crystals from the mesophases well-known
of crystals liquid and motion thermodynamics, Structure, crystals. plastic and transitions of a number
of small and large molecules are discussed. The cooperative nature of the defect equilibrium is
analyzed. Of special interest are the borderlines between liquid high crystals viscosity and condis
crystals and crystals plastic between and posed complications The crystals. condis by pseudorotation,
jumping states symmetry-related between and freezing into non-equilibrium states are illuminated.
Erratum: Vol. 86, p. 143
Editor of the contribution is Prof. Dr. H. H6cker, Aachen
1 Introduction
1.1 Def'mition of Condis Crystals
and an Approximate Empirical Transition Entropy Description
In a recent review of thermotropic mesophases and their transitions )1 it was suggested
that crystals with dynamic conformational disorder do not fit into the standard
classification of mesophases as either plastic crystal s) 2 (with dynamic orientational
disorder and long-range positional order) or liquid crystal )3 (with positional dynamic
disorder and some long-range orientational order). At that time it was proposed
that a distinct third type of mesophase exists, that of the condis crystal (with
dynamic conformational d/sorder and long-range positional and orientational order).
Fig. 1.1 illustrates schematically the various condensed phases and their interrela-
tions. The three classical condensed phases: glass, crystal and melt, are outlined
doubly. Glasses and crystals are considered solid, the melt liquid. Condis crystal,
plastic crystal, and liquid crystal are increasingly less solid (more liquid). The
arrows on the right-hand side indicate the possible transitions between the phases
that are often first order transitions, i.e. transitions that involve a discontinuity
in the first derivative of the Gibbs energy function, the entropy .)4 When starting
with the crystal, the entropy increases going to successively lower states drawn in
Fig. 1.1.
The overall entropy of fusion ASf, of a crystal can be approximately separated
into the three contributions, arising from positional disordering, ASpos, orientational
disordering, , ASorient and conformational disordering, , ASconf so that
(1.1)
ASf = s + ASpo ASorlent + ASconf .
,rtt
SSALG il
-I
SS ACLLG l"
CP SSALG I
DC SSALG l'"
II
CRYSTAL .... !'.,'~
CITSALP LATSYRC
DIUQIL LATSYRC
[L--
Fig. 1,1. Schematic diagram of the relationship
betwteheen three limiting phases (double outline)
MELT
and the six mesophases. Adapted from ) Ref. ~
2 .B hcilrednuW et .ta
It is possible to make a first judgment of a phase classification based on the
thermal analysis of the first order transitions. Such analysis is helped by the empirical
"rules" that sopSA is generally 7-14 J/(K mol) (Richards' rule) .)5 AS ° tn~i is usually
20-50 J/(K mot) (based on Walden's rule) ,)6 and fnocSA is about 7-12 J/(K mol) .)7
While opSA ~ and ASorie,t are referred to the whole molecule, i.e. they do not
change with size; fnncSA is referred to a flexible bond (or a rigid bead), i.e. for
a molecule, AS o,f is size-dependent. The rather broad ranges of values indicate
the approximate nature of this description. For a more precise analysis, effects of
disorder, volume change, changes in vibrational frequency etc. would have to be
detailed. Nevertheless, the empirical rules permit estimations of thev arious transition
entropies corresponding to the arrows of the right-hand side of Fig. 1.1. Particularly
well obeyed is a transition entropy of 7-14 J/(K mol) for the transition from the
plastic crystal to the melt .~2 The analogous transitions from the liquid crystalline
phase to the melt are always much less than ASorlent , indicative of the rather high
degree of orientational disorder and mobility in liquid crystals 1) Condis crystals,
finally, are expected to show variable entropies of transition from the crystal to
the condis-crystal and from the condis-crystal to the isotropic melt, depending on
the type and concentration of conformational disorder.
On cooling, the mesophases do not always follow the equilibrium path. If the
ordering to the crystal can be by-passed, the liquid-like cooperative motion of the
mesophases freezes at a glass transition, as is indicated on the left side of Fig. 1.1.
At these glass transitions there is no change in order and, as a result, no change in
entropy. Since the liquid-like motion changes at the transition to practically only
vibrational motion, there a is drop in heat capacity on vitrification. For liquid crystals,
the existence of the glassy state was already implied in the work of Vorlaender ~8
Their drop in heat capacity is practically identical to those for liquids ~1 For plastic
crystals, the glassy state was first recognized by Adachi, Suga, and Seki .~9 The
order of magnitude of the change in heat capacity at the glass transition of plastic
crystals is also not much different from that of liquids. For the typical glass transition
of a liquid it was found that the change in heat capacity is approximately
10-20 J/(K mol) when calculated per mole of mobile parts (beads) within the
molecule .)01 Since condis crystals show usually intermediate heat capacities between
the solid and liquid states, their change in heat capacity on vitrification is expected to
be variable also.
In this discussion at attempt will be made to describe in greater detail the
structure and motion for a larger number of condis crystals. A special effort will be
made to point-out the differences between condis crystals on the one hand, and
liquid and plastic crystals on the other. It seems reasonable, and has been illustrated
on several examples, that molecules with dynamic, conformational disorder in the
liquid state show such conformational disorder also in the liquid crystalline and
plastic crystalline states H). The major need in distinguishing condis crystals from
other mesophases is thus the identification of translational motion and positional
disorder of the molecular centers of gravity in the case of liquid crystals, and of
molecular rotation in the case of plastic crystals.
Polymorphism is known for mesophases as well as for crystals. It can be considered
a subdivision of the scheme of Fig. 1.1. In most cases it is easy to identify the
polymorphs as one of the four crystal phases, altough particularly some of the
Conformational Motion and Disorder in Low and High Molecular Mass Crystals 3
highly ordered smectic liquid crystals are difficult to distinguish from crystals or
condis crystals as long as a detailed knowledge of structure, motion and thermo-
dynamics is not available. Little can be offered in this review to resolve such problems
of polymorphism.
1.2 Justification of the Empirical Transition Entropy Description
To find an explanation for Richards' rule discussed in Sect. 1.1, one may postulate
that the liquid state possesses a short-range "quasi-crystalline" structure J2). As the
temperature increases, this structure changes gradually, to become "quasi-gaseous"
close to the critical temperature .)21 The meltingp rocess may be, based on this model,
broken into three major steps. First, the crystal lattice is expanded to give the
average separation of the motifs as it exists in the melt. Next, the motifs are
dynamically disordered. Last, defects are introduced into the quasi-crystalline melt.
Starting from a cubic close-packed crystal Lennard-Jones and Devonshire computed
the three melting stages assuming interstitial atoms as defects la~ For argon an
entropy of fusion of 1.70 R, or 14.1 J/(K mol), was computed that matches the
experimental equilibrium value of 14.0 J/(K mol) at 83.8 K. The entropy increase
in going from fixed motifs in the small volume element of the crystal to the total
volume of the melt (communal entropy) was earlier found to be R, or 8.31 J/(K
mol) ~41 The lower and upper limit of Richards' rule seem thus reasonable.
In analogy to the estimates of opSA ,s it is possible to suggest that the empirically
observed values for fnocSA can be linked to the commonly used "rotational isomeric
states" model of linear macromolecutes ~5-17). Assuming two to four rotational
isomers to become dynamically accessible on a disordering transition and % 75 of the
total entropy change to be conformational, one expects an entropy gain of 7.7 to
15,3 J/(K mol), the correct size range of the experimental values. On the basis of
atomistic calculations, a detailed rotator model was analyzed for the condis phase
of flexible linear macromolecules using a cooperative statistical treatment la~. Both,
the transition from the crystal to the condis crystal and from the condis crystal to the
melt coulbde described quantitatively for polyethylaennde for trans-t,4-polybutadiere
as a function of pressure. The overall melting of macromolecules was treated as an,
at least, two-step transition: a conformational transition and the cooperative formation
of dislocations, the latter giving rise to only minor changes in conformation )o2,91
For the condis states of polyethylene and possibly also trans-l,4-polybutadiene the
two steps occur largely separated at thet wo equilibrium transition temperatures d T and
i T (disordering and isotropization temperatures, respectively).
The orientational entropy of fusion ASnrient ~- 20--50 J/(K mol) discussed in Sec t1.. 1
is based on Walden's empirical rule of entropies of irregular, rigid molecules )6
Subtraction of the appropriate s ASp° leads to the suggested values. The separation
of opSA s and ,nelroSA is well documented byt he plastic crystals that often show opSA s as
the isotropization transition 2)
1.3 Motion in the Condensed Phase
The major motion type for the crystalline and glassy solid states is vibration. For linear
macromolecules one finds large deviations from the classical Einstein ~12 or Debye ~22
4 .B hcilrednuW et .la
32 n
2~
C
Jl(Kmol)
16
Fig. 1.2. Computed and experimental heat
capacities of .enerytsylop Glassy solid state A:
skeletal contribution (Tarasov function,
10 = 482 K, 30 = 84 s = K, N ;)6 :B group
contributions gN( = 42); C: total, computed
capacity heat at computed : D volume; constant
and at heat experi- capacity constant pressure
mental points. Liquid state E: experimental
data neewteb transition, glass the T, = 373 K,
and 006 at constant capacity K (heat )erusserp
Temperature )K(
treatments of the heat capacity. Also, an early attempt to approximate the heat
capacities with a combination of a 1-dimensional and 3-dimensional continuum to
account for the anisotropy of the chain molecules )32 was by itself not applicable
over a wide temperature range. The method that was finally successful ,42 )s2 involves
an approximation of the frequency spectrum by separation of the high-frequency
group vibrations from the skeletal chain-vibrations. The group vibrations are then
accessible from normal-mode calculations on isolated chains and are even transferable
for polymers of similar chemical structure. The skeletal vibrations can then be approxi-
mated using the two-parameterT arasov approach 10( and 03) .)32 Agreement between
computation and experiment has been tested for almost 001 polymers and is usually
better than +._ % 5 over the whole temperature range, starting from about 01 K ,62 .)72
Fig. 1.2 illustrates the computed heat capacities of polystyrene, a polymer with six
skeletal vibrations and 48 group vibrations per repeating unit. Within the small scale
of the drawing there is hardly any difference between experiment and compu-
tation 2s).
Also plotted in Fig. 2.1 is the experimental heat capacity of the liquid (at con-
stant pressure) 2s). In simple cases, such as polyethylene, the heat capacity of the
liquid state could be understood by introducing a heat capacity contribution for the
excess volume (hole theory) and by assuming that the torsional skeletal vibration
can be treated as a hindered rotator )92 A more general treatment makes use of a
separation of the partition function into the vibrational part (approximated for
heat capacity by the spectrum of the solid), a conformational part (approximated by
the usual conformational statistics) 15-~7), and an external or configurational part.
The latter was shown to be almost completely represented by the difference of heat
